@acer indeed I did.  I borrowed _maxim_'s answer yes.  But no one was replying I felt forced to create another question in which someone might  bring forth some answers.  If that is frowned upon, then I will refrain.  Sorry.

@_Maxim_ That is absolutely brilliant!  Great work!

How did you determine the mask?

@tomleslie thanks for the in depth explanation.  I understand what needs to be done, but how to put that into maple code?

And now we need to mask and transform back to the spatial plane.

@_Maxim_ ok thanks.  Replacing SignalProcessing:-FFT(img) with DiscreteTransforms:-FourierTransform makes it work.  Thanks

@_Maxim_ I'm using M18 and I get an error after img2 execution.

Error, (in SignalProcessing:-Engine:-FFT) data is not one-dimensional

@tomleslie actually I just copied the page from matlab.  I don't have the image.  But I found one similar on google images - here's the image but mapleprimes won't allow to insert it as a .jpg

**edit added** The file must be zipped to allow a download link to be added.

Interested as well. 

Firstly how do we get from the noisy clown to the spectrum image?

The single quotes are delayed evaluation.  That would be where the confusion is coming from.

a := int(1/((1-(1/4)*t^2)*sqrt(-t^2+1)*sqrt(-4*t^2+1)), t);

                                          /     1      \
                    a := EllipticPi |  t,   - ,  2  | 
                                          \     4      /
evalf(subs(t = 3/2, a));

                  0.1560547979 - 1.261993176 I

For comparison M12 shows the plots as ...

Well that's interesting!  The plots in Maple 12 are shown as black.  However in mapleprimes they're shown in color and in Maple 2017 the last three plots are shown blank. 

For explicit purposes the commands should show

Download shading-none.mw

@Carl Love actually the arrows aren't white otherwise you would see the boxed axes dissappearing as a white arrow passed in front. 

In fact arrows=THICK is the only option that makes shading=none work.  SLIM, LINE, and THIN don't produce any visible change from the empty plot.

Oh, ok.  But with no shading they should be black arrows.  I don't know why it changed to white, there should have been no reason for the programming change.